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We explore how chiral-symmetry constraints on weak-interaction matrix elements point toward the existence of an intermediate-state σ in several different weak-interaction processes. Particular attention is directed toward recent evidence for a σ within three-body nonleptonic weak decays.

The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV. When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces $G/H$ and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in $\mathrm{\text{O}}(N)$ and $\mathrm{\text{CP}}(N-1)$ models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of $\mathrm{\text{O}}(N)$ sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal ${𝒩}=(0,1)$ supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal ${𝒩}=(0,1)$ models with the $S^{N-1}=\mathrm{\text{SO}}(N)/\mathrm{\text{SO}}(N-1)$ target space while preserving the isometries. This also includes $\mathrm{\text{CP}}(1)$ (equivalent to $S^2$) which is an exceptional case from the $\mathrm{\text{CP}}(N-1)$ series. For other $\mathrm{\text{CP}}(N-1)$ models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the $\mathrm{\text{CP}}(N-1)$ models to compare the original of different anomalies. A dual formalism of $\mathrm{\text{O}}(N)$ model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.

In light of the improved precision of the experimental measurements and enormous theoretical progress, the nucleon form factors have been evaluated with an aim to understand how the static properties and dynamical behavior of nucleons emerge from the theory of strong interactions between quarks. We have analyzed the vector and axial-vector nucleon form factors ($G_{E,M}^{p,n}(Q^2)$ and $G_A^{p,n}(Q^2)$) using the spin observables in the chiral constituent quark model ($\chi$CQM) which has made a significant contribution to the unraveling of the internal structure of the nucleon in the nonperturbative regime. We have also presented a comprehensive analysis of the flavor decomposition of the form factors ($G_E^q(Q^2)$, $G_M^q(Q^2)$ and $G_A^q(Q^2)$ for $q=u,d,s$) within the framework of $\chi$CQM with emphasis on the extraction of the strangeness form factors which are fundamental to determine the spin structure and test the chiral symmetry breaking effects in the nucleon. The $Q^2$ dependence of the vector and axial-vector form factors of the nucleon has been studied using the conventional dipole form of parametrization. The results are in agreement with the available experimental data.

The SU(3) Polyakov linear-sigma model (PLSM) in mean-field approximation is utilized in analyzing the chiral condensates ${\sigma }_u$, ${\sigma }_d$, ${\sigma }_s$ and the deconfinement order parameters $\varphi$, $\bar{\varphi }$, at finite isospin asymmetry. The bulk thermodynamics including pressure density, interaction measure, susceptibility and second-order correlations with baryon, strange and electric charge quantum numbers are studied in thermal and dense medium. The PLSM results are confronted to the available lattice quantum chromodynamics (QCD) calculations. The excellent agreement obtained strengthens the reliability of fixing the PLSM parameters and therefore supports further predictions even beyond the scope of the lattice QCD numerical applicability. From the QCD phase structure at finite isospin chemical potential $({\mu }_I)$, we find that the pseudocritical temperatures decrease with the increase in ${\mu }_I$. We conclude that the QCD phase structure in $(T_{\chi }\text{–}{\mu }_I)$ plane seems to extend the one in $(T_{\chi }\text{–}{\mu }_B)$ plane.

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the ’t Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua.

Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies.

Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments.

The process γπ → ππ, in the limit of vanishing photon and pion energies, is determined by the chiral anomaly. This reaction can be investigated experimentally using Primakoff reactions, as currently done at COMPASS. We derive a dispersive representation that allows one to extract the chiral anomaly from cross-section measurements up to 1 GeV, where effects of the ρ resonance are included model-independently via the ππ P-wave phase shift. We discuss how this amplitude serves as an important input to a dispersion-theoretical analysis of the π⁰ transition form factor, which in turn is a vital ingredient to the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.

Dispersion-theoretical analyses of transition form factors are stepping stones to a model-independent determination of the light-by-light scattering contribution to (g - 2)_μ. We extend a calculation of the conversion decays of the lightest isoscalar vector mesons, ω/ϕ → π⁰ℓ⁺ℓ^-, that builds on a previous dispersive analysis of the ω/ϕ → 3π partial-wave amplitudes and the pion vector form factor as its sole ingredients. We construct a good parametrization of e⁺e^- → 3π that, together with information on the anomalous process γπ → ππ, allows us to obtain a description of the π⁰ transition form factor measured in e⁺e^- → π⁰γ.

The goal of the DIRAC experiment at CERN (PS212) is to measure the π⁺π^- atom lifetime. Based on part of the collected data we present a first result on the lifetime, , and discuss the major systematic errors. This lifetime corresponds to .

The X(3872) is a charmonium-like hadron with a mass close to the threshold. It was first observed in 2003 by the Belle Collaboration and confirmed shortly after by the CDF collaboration. The quantum numbers were recently determined by the LHCb experiment to be J^PC = 1⁺⁺³. Yet, the nature of the X(3872) is not fully understood. In future, lattice QCD calculations should be able to obtain observables and are expected to contribute to a better understanding of the X…